Calibrated Similarity for Reliable Geometric Analysis of Embedding Spaces
This work addresses the limited interpretability of cosine similarity in pretrained embedding spaces, where absolute similarity values are concentrated in a narrow range due to anisotropy. The authors propose a monotonic calibration method based on isotonic regression that reparameterizes similarity scores without altering the underlying embeddings or their geometric structure. The approach strictly preserves the original ranking order of similarities, thereby maintaining all ordinal-dependent structures—such as nearest neighbors, angular rankings, and threshold graphs—intact. The calibrated similarities achieve near-perfect alignment in absolute values while retaining 98% local stability under seven types of perturbations and fully preserving rank correlation with the original similarities.